Static voltage safety domain construction and voltage regulation method and device for medium-voltage power distribution network and medium

Abstract

The invention discloses a medium-voltage power distribution network static voltage safety domain construction and voltage regulation method and device and a medium. The medium-voltage power distribution network static voltage safety domain construction method comprises the steps of constructing a medium-voltage power distribution network static voltage safety domain based on a physical model; obtaining a hyperplane boundary model of the static voltage safety domain of the medium-voltage power distribution network based on historical operation data of the medium-voltage power distribution network; processing the hyperplane boundary model of the static voltage safety domain of the medium-voltage distribution network by adopting a stochastic chance constraint linear voltage optimization method to obtain a stochastic chance constraint model of the static voltage safety domain of the medium-voltage distribution network; and on the basis of the stochastic chance constraint model, constructing a medium-voltage power distribution network node voltage optimization model, and performing optimization control on the real-time voltage of the medium-voltage power distribution network node by using the model. The method gets rid of dependence on accurate physical parameters, visualization of the security domain can still be achieved under the condition that the parameters are incomplete, and the calculation efficiency is remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power distribution network operation control, and more particularly to a medium-voltage power distribution network static voltage safety domain construction and voltage regulation method and device and medium. BACKGROUND

[0002] Global energy transformation promotes large-scale access of distributed photovoltaics to medium-voltage power distribution networks, but the intermittency and randomness of photovoltaic output change the traditional "passive" operation characteristics of power distribution networks, leading to prominent static voltage safety problems, and accurate and efficient safety analysis models are needed to support operation decisions.

[0003] Static voltage safety domain (SVSR) is a core tool for depicting voltage safety boundaries and can provide a basis for operation optimization, and its construction relies on accurate power flow calculation. Traditional power flow calculation is based on a physical model and achieves state assessment by solving a nonlinear equation set of node voltage and injected power.

[0004] In the high-penetration photovoltaic access scenario, the traditional method has obvious shortcomings: first, the parameters of the power distribution network are difficult to obtain completely due to limitations such as measurement conditions and update lag, resulting in large calculation errors; second, the fluctuation of photovoltaic output increases the uncertainty of injected power, and the traditional method has poor adaptability and low efficiency, which cannot meet the real-time monitoring requirements.

[0005] Improved methods such as decoupled linear power flow (DLPF) and sensitivity-based linear power flow (SLPF) have improved efficiency through linearization, but still rely heavily on accurate network parameters, and the precision drops sharply when parameters are missing or have errors, which cannot provide reliable support for SVSR construction. Existing SVSR construction also faces bottlenecks: complete topology information and accurate parameters are needed, and a large number of power flow calculations are required to traverse the safety boundary, with extremely high computational complexity. After high-penetration photovoltaics intensify parameter uncertainty, the applicability and efficiency of traditional methods further decline, making it difficult to update and visualize quickly.

[0006] In summary, existing methods generally have high parameter dependence, poor uncertainty adaptation, and low calculation efficiency, making it difficult to support safe operation of power distribution networks under high-penetration photovoltaic and storage access. Developing an SVSR modeling method that does not rely on accurate physical parameters, adapts to power fluctuations, and is efficient is an urgent need in the field. SUMMARY

[0007] To overcome the shortcomings of existing technologies and address issues such as incomplete parameters, uncertainty in node injected power, and model solvability in medium-voltage distribution networks, this invention proposes a method, device, and medium for constructing and regulating the static voltage safety domain (SVSR) of medium-voltage distribution networks based on data-driven probabilistic power flow. By employing high-dimensional state-space mapping technology, the nonlinear power flow equations are transformed into linear expressions, and historical data is used to train the state-space matrix, eliminating the dependence on precise physical parameters. This method derives the hyperplane boundary expression for the SVSR, enabling visualization of the safety domain even with incomplete parameters. Furthermore, by combining the semi-invariant method and Cornish-Fisher expansion, probabilistic chance constraints are transformed into a linear combination of node injected power, significantly improving computational efficiency.

[0008] The objective of this invention can be achieved through the following technical solutions.

[0009] A method for constructing and regulating the static voltage safety domain of a medium-voltage distribution network includes the following steps: S1, Constructing the static voltage security domain of the medium-voltage distribution network based on the physical model; S2, Based on historical operating data of the medium-voltage distribution network, obtain the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network mentioned above; S3. The stochastic chance constrained linear voltage optimization method is used to process the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network to obtain the stochastic chance constrained model of the static voltage security domain of the medium-voltage distribution network. S4. Based on the above stochastic chance constraint model, a voltage optimization model for medium-voltage distribution network nodes is constructed, and this model is used to optimize and control the real-time voltage of medium-voltage distribution network nodes.

[0010] Furthermore, the definition of the static voltage security domain of the medium-voltage distribution network in step S1 is as follows: (1), In the formula, ; , representing any node in a medium-voltage distribution network The static voltage safety domain It is the set of all nodes in a medium-voltage distribution network; This represents the AC power flow equations at the root node under specified voltage magnitudes and phase angles. This represents the parameters of the equation; This represents a column vector composed of the voltages of each node in a medium-voltage distribution network. This represents a column vector composed of the minimum voltage values ​​at each node of a medium-voltage distribution network. This represents a column vector composed of the maximum voltage values ​​of each node in a medium-voltage distribution network.

[0011] Furthermore, the expression for the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network described in step S2 is as follows: (2), In the formula, , representing the load power within a specific time period, vector and These represent column vectors composed of the active and reactive power of each branch in the medium-voltage distribution network, respectively. and The upper and lower limits of the hyperplane coefficients in the hyperplane boundary of the static voltage security domain of any node i in a medium-voltage distribution network are represented. and These represent the critical points at the upper and lower limits of active power, respectively. and These represent the critical points at the upper and lower limits of reactive power, respectively. This represents the function for dimension upscaling. and M1 and M2 represent the dimensionality-upgrading operation functions for the upper and lower critical points, respectively; M1 and M2 represent matrices, with M1 handling power differences and M2 handling nonlinear changes in the power grid state.

[0012] Furthermore, in step S3, a stochastic chance constrained linear voltage optimization method is used to process the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network to obtain a stochastic chance constrained model of the static voltage security domain of the medium-voltage distribution network. The specific process is as follows: At confidence level Under these conditions, ensure the voltage V at node j of the medium-voltage distribution network. j Not exceeding the upper limit or lower limit The general expression for opportunity constraints is: (3), In the formula, Let be a probability function. and These represent the confidence levels for the upper and lower limits of the voltage constraints at node j, respectively. If we use column vectors and If the active and reactive power regulation of a node are represented respectively, then the model optimization process must follow the following constraints: (4), (5) In the formula, G represents the set of nodes with controllable active power devices; H represents the set of nodes with controllable reactive power devices. and These represent the active power injection and reactive power injection at node j, respectively. and These represent the predicted active and reactive power injection values ​​for node j, respectively. This represents the active power adjustment amount at node j; This represents the reactive power adjustment amount at node j; Combining equations (3)-(5) with the hyperplane boundary model expression of the static voltage security domain of the medium-voltage distribution network, we obtain: (6), In the formula, and Let represent the upper and lower bounds of the decision factors for node j, respectively. and These represent the reference active power and the reference reactive power, respectively. make , Formula (6) simplifies to the following formula (7): (7), For a given Define the injection power probability distribution function for node j as follows. : (8), Combining formulas (7) and (8), the opportunity constraints for safe voltage operation can be expressed as the following upper and lower limits: (9), Given Having a monotonically increasing property, equation (9) can be equivalently transformed into equation (10): (10) In the formula, for The inverse function; let The solution process is achieved through a combination of semi-invariant methods and Cornish-Fisher series expansion. The specific steps are as follows: Step S31: According to and Calculate the corresponding k-th order raw moments respectively. and ; Step S32: Based on the functional relationship between the different orders of semi-invariants and the origin moments shown in equation (11), calculate the k-th order semi-invariants of the predicted active and reactive power values ​​at node j. and ; (11), Step S33: Calculate the node voltage magnitude The k-th order semi-invariant; if the random variables are independent, their semi-invariants have the following linear properties: node voltage amplitude The k-th order semi-invariant can be calculated from the semi-invariants of the node injected power. (12), In the formula, This represents the power of node j at time k. This represents the coefficients associated with node j. and Indicates at time Time node Active power and reactive power, It is the set of all nodes in a medium-voltage distribution network. Indicates the total number of nodes; Step S34: Calculate the node voltage magnitude based on semi-invariants and Cornish-Fisher expansion method ; (13) In the formula, , It is the standard normal distribution function; Formula (10) is solved through the linear optimization process of formulas (11)-(13) above to determine the upper and lower limits of the voltage at node j. and The corresponding chance constraint linear expressions for the upper and lower limits of the voltage at node j are obtained as follows (14), which is the stochastic chance constraint model of the static voltage security domain of the medium voltage distribution network. (14) In the formula, and Representing nodes respectively j The upper and lower limits of the decision factors; and A column vector representing the active and reactive power regulation of each node; and Representing nodes respectively j Upper and lower limits of voltage.

[0013] Furthermore, the medium-voltage distribution network node voltage optimization model in step S4 includes an objective function and constraints. The objective function expression of the medium-voltage distribution network node voltage optimization model is as follows: (15) The constraint expressions for the medium-voltage distribution network node voltage optimization model are as follows: (16) In the formula, and These are column vectors representing the active and reactive power regulation quantities of each node, respectively. This represents the active power adjustment amount at node j; This represents the reactive power adjustment amount at node j; and Representing nodes respectively j The upper and lower limits of active power injection; and Representing nodes respectively j The upper and lower limits of reactive power injection; and These represent the predicted active and reactive power injection values ​​for node j, respectively. Indicates the current tap position of the on-load tap changer; and These represent the lower and upper limits of the on-load tap changer position, respectively. A column vector representing the rated voltage of each node; This represents a column vector composed of the voltage magnitudes of each node; This indicates the operating cost coefficient of the on-load tap changer; and These are auxiliary variables representing the positive and negative changes in the on-load tap changer position, respectively. M 1,j and M 2,j These represent two matrices, one for handling power differences and the other for handling nonlinear changes in grid conditions. and These represent the reference active power and the reference reactive power, respectively. ; This represents the function for dimension upscaling. Indicates the reference current; β 1 represents the coefficient between the change in current or power and the power adjustment; Indicates the upper limit of the line current; and These represent the active power and reactive power transmitted from node i to node j, respectively. and These represent the active power and reactive power transmitted from node j to node k, respectively. and Let G and H represent the active power injection and reactive power injection at node j, respectively; G represents the set of nodes with controllable active power devices; H represents the set of nodes with controllable reactive power devices. It is the set of all nodes in a medium-voltage distribution network; Let represent the set of downstream adjacent nodes of node j in a medium-voltage distribution network.

[0014] The objective of this invention can also be achieved through the following technical solutions.

[0015] A device for constructing and regulating the static voltage safety domain of a medium-voltage distribution network includes: Static voltage security domain physical construction module: Constructs the static voltage security domain of medium-voltage distribution network based on physical model; Static voltage security domain data construction module: Based on historical operating data of medium-voltage distribution network, obtain the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network mentioned above; Stochastic chance constraint model construction module: The stochastic chance constraint linear voltage optimization method is used to process the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network to obtain the stochastic chance constraint model of the static voltage security domain of the medium-voltage distribution network. Node voltage optimization module: Based on the above stochastic chance constraint model, a node voltage optimization model for medium-voltage distribution network is constructed, and this model is used to optimize and control the real-time voltage of the nodes in the medium-voltage distribution network.

[0016] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the above-described method for constructing and regulating the static voltage safety domain of a medium-voltage distribution network.

[0017] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method for constructing and regulating the static voltage safety domain of a medium-voltage distribution network.

[0018] Compared with existing technologies, the beneficial effects of the technical solution of the present invention are as follows: Static voltage stability domain is a key indicator for optimizing the operation of medium-voltage distribution networks with a high proportion of distributed generation. The method proposed in this invention effectively addresses the shortcomings of existing power flow calculation methods, static voltage stability domain generation methods, and distributed generation uncertainty management methods. The main research results are as follows: (1) Based on historical operating data of medium-voltage distribution networks, this invention establishes a hyperplane boundary model of the static voltage security domain of medium-voltage distribution networks. The modeling process is data-driven based on high-dimensional state-space mapping, eliminating the dependence of traditional power flow calculations on precise physical parameters. Compared with distributed linearization and simplified linearization power flow algorithms, it has higher computational accuracy and can more accurately achieve voltage regulation targets. Compared with the static voltage stability domain based on precise AC power flow models, its maximum boundary error is only 0.741%, and the proposed method can better meet the needs of practical engineering applications.

[0019] (2) A voltage optimization model for medium-voltage distribution network nodes integrating static voltage security domain and stochastic chance constraints was constructed. Compared with point-to-point adjustment methods, this model implements voltage regulation from a regional perspective, avoiding the computational burden caused by frequent power flow calculations under high-proportion renewable energy access. Compared with uncertainty management methods such as Monte Carlo simulation or scenario generation, the proposed method achieves linearization of probabilistic constraints in the data-driven power flow model by combining semi-invariants with the König-Fischer expansion method, greatly simplifying the voltage optimization model structure. While ensuring computational accuracy, computational efficiency is significantly improved, enabling rapid assessment of voltage security and meeting the rapid decision-making needs in practical applications.

[0020] (3) Although existing data-driven methods can approximate the generation of the safety domain, they lack rigorous mathematical interpretation and are difficult to couple with the voltage optimization model of medium-voltage distribution network nodes. The static voltage safety domain model proposed in this invention provides strict guarantees of uniqueness and convexity, ensuring continuity and consistency, and laying a solid mathematical foundation for the coupling of optimization models.

[0021] (4) This invention constructs a data-driven hyperplane boundary model expression for the static voltage security domain boundary through high-dimensional state-space mapping (Formula 16). This model does not rely on network parameters, providing a model-free solution for medium-voltage distribution network optimization. Based on the data-driven hyperplane boundary model for the static voltage security domain boundary, this invention derives a stochastic chance constraint model for the static voltage security domain of medium-voltage distribution networks (Formula 28), solving the visualization problem of the security domain when distribution network parameters are incomplete. This method provides the possibility of real-time assessment of system operation safety by determining the location of the operating point within the region, thus providing an important basis for decision-making. This invention simplifies the complex probabilistic chance constraints of node voltages into a linear combination of node injected power through the hyperplane expression of the security domain boundary, effectively resolving the contradiction between power injection uncertainty and computational efficiency. Attached Figure Description

[0022] Figure 1 This is an improved IEEE 33-node distribution network topology diagram in an embodiment of the present invention.

[0023] Figure 2 These are the voltage regulation optimization results of the three power flow methods in the IEEE-33 node system in the embodiments of the present invention.

[0024] Figure 3 These are the verification results of the optimized solutions of the three power flow methods in the embodiments of the present invention (using precise nonlinear power flow verification).

[0025] Figure 4 This is a static voltage safety domain distribution diagram of nodes 12 and 15 on a two-dimensional cross section (P11, P14) in an embodiment of the present invention.

[0026] Figure 5 This is a comparison diagram of the maximum error of the two-dimensional cross-section (P11, P14) in the embodiment of the present invention.

[0027] Figure 6 This is a current distribution diagram of different lines in an embodiment of the present invention.

[0028] Figure 7 This is a diagram showing the position change of the operating point in the two-dimensional cross section of the SVSR during the voltage regulation process in this embodiment of the invention.

[0029] Figure 8 This is a voltage probability distribution diagram of weak nodes in a medium-voltage distribution network after voltage optimization according to an embodiment of the present invention. Detailed Implementation

[0030] The present invention will now be further described with reference to the accompanying drawings.

[0031] The present invention provides a method for constructing and regulating the static voltage safety domain of a medium-voltage distribution network, which specifically includes the following steps S1 to S4.

[0032] S1, constructing the static voltage security domain of the medium-voltage distribution network based on the physical model.

[0033] set up It is the set of all nodes in a medium-voltage distribution network. For the set of feeders, where the feeders are... Connect node i and node j. The reference node for a medium-voltage distribution network (MVDN) is represented by node 0. In terms of state variables, This represents the voltage magnitude at node i. This represents the voltage magnitude at node j, while and These represent the active power injection and reactive power injection at node j, respectively. Feeder The resistance and reactance are denoted as follows: and The active and reactive power transmitted from node i to node j are respectively represented by... and In addition, let's assume... Let i be the set of all downstream adjacent nodes of node i.

[0034] The operating conditions of medium-voltage distribution networks are determined by variables. Characterization. This invention is applicable to medium-voltage distribution network operating conditions. Within the constructed nodal power injection space, the static voltage security domain is presented. The static voltage security domain is formed by mapping the voltage and power relationships of each node into a multi-dimensional space, creating a boundary region where operating points represent a voltage-safe state. The nodal power injection space is a type of Euclidean space, a mathematical space used to represent the state variables such as voltage and power of each node in a power distribution network. This high-dimensional mapping provides a foundation for modeling the static voltage security domain of the distribution network.

[0035] The power flow equations in the physical model of a medium-voltage distribution network can be expressed as: (1), The operating constraints in the physical model of a medium-voltage distribution network can be expressed as follows: (2), In the formula, the superscripts max and min represent the upper and lower limits of the variable, respectively; and Representing nodes respectively The minimum and maximum values ​​of the voltage represent the safe range of the node voltage; and These represent the active power injection and reactive power injection at node i, respectively. and The minimum and maximum values ​​of active power injection at node i are respectively; and Let G be the minimum and maximum values ​​of reactive power injection at node i, respectively; G is the set of nodes with controllable active power devices, and H is the set of nodes with controllable reactive power devices.

[0036] Given the actual operating conditions of medium-voltage distribution networks, the analysis focuses on the power injection space located at nodes. When considering the static voltage safety domain, only the voltage from the normal initial operating point is considered. The area enclosed by the safety boundary first encountered during outward expansion. Within the defined nodal power injection space, any node of the medium-voltage distribution network... Static voltage safety domain Defined as: (3), In the formula, ; This represents the AC power flow equations at the root node under specified voltage magnitudes and phase angles. This represents the parameters of the equation.

[0037] Therefore, the definition of the static voltage safety domain for medium-voltage distribution networks is: (4), In the formula, ; vector This represents a column vector composed of the voltages of each node in a medium-voltage distribution network. This represents a column vector composed of the minimum voltage values ​​at each node of a medium-voltage distribution network. This represents a column vector composed of the maximum voltage values ​​of each node in a medium-voltage distribution network.

[0038] S2. Based on historical operating data of the medium-voltage distribution network, the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network is obtained.

[0039] Given that medium-voltage distribution networks typically have a radial topology, according to equation (1), ignoring network losses and linearizing the square term, a linear relationship between node voltage and node power can be obtained, as shown in equation (5): (5), To linearize the power flow equations of equation (5) into matrix form, let This represents the complete node-branch correlation matrix of a medium-voltage distribution network. From the matrix... After removing the first row corresponding to reference node 0, the remaining part forms a new full-rank matrix, which serves as the new node-branch association matrix. Based on node-branch association matrix The equations for active power and reactive power can be expressed in the following matrix form: (6), (7), In the formula, column vector and Each branch active power and reactive power Composition. Vector and It is a column vector composed of the active and reactive power of each branch in the power grid. The branch voltage equation can be expressed in the following matrix form: (8), In the formula, Represents the reference voltage vector of the system, vector This represents a column vector composed of the voltages of each node in a medium-voltage distribution network. Representation matrix The first row. Matrix and It is a diagonal matrix, and its diagonal elements are as follows: and All other elements are zero, T represents the transpose of the matrix, and -T represents the inverse transpose of the matrix. Substituting equations (6) and (7) into equation (8) and simplifying, we can obtain the linear relationship between node voltage and node power, as shown in equation (9).

[0040] (9), in, , and Let represent resistance, reactance, and voltage, respectively. Equation (5) provides the basic linear relationship between voltage and power, while Equation (9) further specifies this relationship, typically expressed in matrix form as a linear mapping between voltage and power. It is evident that the matrix... and This accurately describes the linear relationship between node power and node voltage. According to Koopman theory, nonlinear equations can be precisely mapped to linear equations in a high-dimensional Hilbert space. Therefore, we employ a high-dimensional state-space mapping method to construct a high-precision power flow model, thereby more accurately describing the linear relationship between node voltage and node power. Specifically, the nonlinear power flow equations in a medium-voltage distribution network can be expressed as follows: (10) In the formula, The linearized approximation describing the nonlinear power flow process in the power grid, equation (9), is obtained by linearizing the nonlinear power flow equation of equation (10). Output variables and input variables Both consist of active power and reactive power. This is achieved by constructing a depth-first search (DL) function. And train the state-space mapping (SSM) matrix. The relationship between output and input variables can be described as follows: (11), In the formula, x lift This represents a new state vector obtained through the dimensionality-upgrading method, which helps to transform the behavior of a nonlinear system into the form of a linear system.

[0041] Different dimension-up operations require different basis vectors. The details are as follows: (12), in, Indicates the first The expression for the dimension-up operation function of the extended dimension basis vectors is: (13) In the formula, Representing vectors The j-th element in Represents basis vectors The j-th component, where A represents the dimension of the input variable. This is achieved by performing a state-space mapping matrix on a large amount of historical sample data. The least squares estimation yields the upgraded linear power flow equation (DL-PF). This equation is obtained through the state-space mapping matrix. Describe the linear relationship between power injection and bus voltage: (14) In the formula, This represents the load power within a specific time period, consisting of active power and reactive power, and is a vector. and These represent column vectors consisting of the active and reactive power of each branch in the medium-voltage distribution network, respectively. They can be considered constant values ​​during single-time period optimization. Next, we will consider the nodes in the medium-voltage distribution network (MVDN). The voltage amplitude problem, assuming and These represent the upper and lower limits of the injected power at this node. Then, at the voltage... or Under certain conditions, the hyperplane expression for the corresponding voltage limit can be derived: (15) In the formula, and These represent the critical points at the upper and lower limits of the node voltage, respectively. and These represent the critical points at the upper and lower limits of active power, respectively. and These represent the critical points at the upper and lower limits of reactive power, respectively. This represents the function for dimension upscaling. and M1 and M2 represent the dimensionality-upgrading operation functions for the upper and lower critical points, respectively; M1 and M2 represent matrices, with M1 handling power differences and M2 handling nonlinear changes in the power grid state.

[0042] After normalizing equation (15), the expression for the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network can be obtained as follows: (16) In the formula, ; and The upper and lower limits of the hyperplane coefficients represent the hyperplane boundary of the static voltage security domain of any node i in a medium-voltage distribution network.

[0043] S3. A stochastic chance-constrained linear voltage optimization method is used to process the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network, obtaining a stochastic chance-constrained model of the static voltage security domain of the medium-voltage distribution network. The specific process is as follows: The impact of nodal power injection on voltage operating constraints is typically expressed probabilistically. Such constraints are difficult to explicitly characterize using nodal power injection. Based on the Static Voltage Stability Region (SVSR), this invention proposes a stochastic chance-constrained linear voltage optimization method to address the uncertainty of nodal power injection in medium-voltage distribution networks. At a confidence level... Under these conditions, ensure the voltage V at node j of the medium-voltage distribution network. j Not exceeding the upper limit or lower limit The general expression for opportunity constraints is: (17) In the formula, Let be a probability function. and These represent the confidence levels of the upper and lower voltage constraints at node j, respectively.

[0044] In the voltage optimization model of medium-voltage distribution network nodes, the active and reactive power of adjustable nodes can be adjusted in real time to ensure that the voltage meets the confidence level requirements of the chance constraint under all operating scenarios. If represented by a column vector... and If the active and reactive power regulation of a node are represented respectively, then the model optimization process must follow the following constraints: (18) (19) In the formula, G represents the set of nodes with controllable active power devices; H represents the set of nodes with controllable reactive power devices. and These represent the active power injection and reactive power injection at node j, respectively. and These represent the predicted active and reactive power injection values ​​for node j, respectively. This represents the active power adjustment amount at node j; This represents the reactive power adjustment amount at node j.

[0045] Combining equations (17)-(19) with the hyperplane boundary model expression (16) of the static voltage security domain of the medium-voltage distribution network, we can obtain: (20) In the formula, and Let represent the upper and lower bounds of the decision factors for node j, respectively. and These represent the reference active power and the reference reactive power, respectively.

[0046] Simplify equation (20) by letting , Equation (21) can be obtained: (twenty one), For a given Define the injection power probability distribution function for node j as follows. : (twenty two), Combining equations (21) and (22), the opportunity constraint for safe voltage operation can be expressed as the following upper and lower limits: (twenty three), Given Having a monotonically increasing property, equation (23) can be equivalently transformed into equation (24): (twenty four), In the formula, for The key to establishing this constraint is determining the upper and lower limits of the inverse function of the node injection power probability distribution. and The value taken at the corresponding confidence level.

[0047] To simplify the expression, let It should be noted that only the following information needs to be obtained during modeling: Numerical solutions do not require explicit expression. The solution process is achieved through a combination of semi-invariant methods and Cornish-Fisher series expansion. The specific steps are as follows: Step S31: According to and Calculate the corresponding k-th order raw moments respectively. and .

[0048] Step S32: Based on the functional relationship between the semi-invariants of different orders and the moment at the origin shown in equation (25), calculate the k-th order semi-invariant of the predicted active and reactive power values ​​at node j. and .

[0049] (25) In the formula, and Let represent the first-order semi-invariants of the predicted active and reactive power values ​​at node j, respectively. and Let represent the nth-order semi-invariants of the predicted active and reactive power values ​​at node j, respectively.

[0050] Step S33: Calculate the node voltage magnitude The k-th order semi-invariants. If the random variables are independent, their semi-invariants have the following linear properties: Node voltage amplitude The k-th order semi-invariant can be calculated from the semi-invariants of the node injected power.

[0051] (26) In the formula, This represents the power of node j at time k. This represents the coefficients associated with node j. and Indicates at time Time node Active power and reactive power, It is the set of all nodes in a medium-voltage distribution network. This represents the total number of nodes.

[0052] Step S34: Calculate the node voltage magnitude based on semi-invariants and Cornish-Fisher expansion method .

[0053] (27) In the formula, , It is the standard normal distribution function.

[0054] Equation (24) is solved through the linear optimization process of equations (25)-(27) above to determine the upper and lower limits of the voltage at node j. and The corresponding chance constraint linear expressions for the upper and lower limits of the voltage at node j are obtained as follows (14), which is the stochastic chance constraint model of the static voltage security domain of the medium voltage distribution network. (28) In the formula, and Representing nodes respectively j The upper and lower limits of the decision factors; and The column vectors represent the active and reactive power regulation of each node.

[0055] S4. Based on the above stochastic chance constraint model, a voltage optimization model for medium-voltage distribution network nodes is constructed, and this model is used to optimize and control the real-time voltage of medium-voltage distribution network nodes.

[0056] Based on the established voltage opportunity constraint model (28), an optimization function is constructed with the objective of minimizing voltage deviation and the number of on-load tap changer (OLTC) tap position adjustments. Its mathematical expression is as follows: (29) in, A column vector representing the rated voltage of each node. The operating cost factor for on-load tap changers (OLTC) and These represent the current gear and the initial gear of the OLTC, respectively.

[0057] Substitute equations (14) and (18) into equation (29), and then... After relaxation, the optimization problem can be formulated as having adjustable active power. Adjustable reactive power and tap changer positions It is a function of the decision variables.

[0058] Therefore, the objective function expression of the medium-voltage distribution network node voltage optimization model is as follows: (30) The constraint expressions for the medium-voltage distribution network node voltage optimization model are as follows: (31), In the formula, and These are column vectors representing the active and reactive power regulation quantities of each node, respectively. This represents the active power adjustment amount at node j; This represents the reactive power adjustment amount at node j; and Representing nodes respectively j The upper and lower limits of active power injection; and Representing nodes respectively j The upper and lower limits of reactive power injection; and These represent the predicted active and reactive power injection values ​​for node j, respectively. Indicates the current tap position of the on-load tap changer; and These represent the lower and upper limits of the on-load tap changer position, respectively. A column vector representing the rated voltage of each node; This represents a column vector composed of the voltage magnitudes of each node; This indicates the operating cost coefficient of the on-load tap changer; and These are auxiliary variables representing the positive and negative changes in the on-load tap changer position, respectively. M 1,j and M 2,j These represent two matrices, one for handling power differences and the other for handling nonlinear changes in grid conditions. and These represent the reference active power and the reference reactive power, respectively. This represents the function for dimension upscaling. Indicates the reference current; β 1 represents the coefficient between the change in current or power and the power adjustment; Indicates the upper limit of the line current; and These represent the active power and reactive power transmitted from node i to node j, respectively. and These represent the active power and reactive power transmitted from node j to node k, respectively. and Let G and H represent the active power injection and reactive power injection at node j, respectively; G represents the set of nodes with controllable active power devices; H represents the set of nodes with controllable reactive power devices. Let be the set of all nodes in a medium-voltage distribution network. This parameter can be treated as a constant. Let represent the set of downstream adjacent nodes of node j in a medium-voltage distribution network. Equations (29)-(30) are for controllable variables. and It takes the form of a linear combination and uses linear integer programming techniques to efficiently solve optimization problems related to power grid operation, ensuring that the power grid achieves its optimal operating state while meeting current, voltage, and transformer regulation constraints.

[0059] Based on the principles of the above-mentioned method for constructing and regulating the static voltage security domain of medium-voltage distribution networks, this invention also proposes a device for constructing the static voltage security domain of medium-voltage distribution networks, which mainly includes: a physical construction module for the static voltage security domain, a data construction module for the static voltage security domain, a random chance constraint model construction module, and a node voltage optimization module.

[0060] The static voltage security domain physical construction module constructs the static voltage security domain of the medium-voltage distribution network based on the physical model, as detailed in step S1 of the above method.

[0061] The static voltage security domain data construction module obtains the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network based on historical operating data of the medium-voltage distribution network. See step S2 in the above method for details.

[0062] The stochastic chance constraint model construction module uses a stochastic chance constraint linear voltage optimization method to process the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network, thereby obtaining a stochastic chance constraint model of the static voltage security domain of the medium-voltage distribution network. See step S3 in the above method for details.

[0063] The node voltage optimization module, based on the aforementioned stochastic chance constraint model, constructs a medium-voltage distribution network node voltage optimization model, and uses this model to optimize and control the real-time voltage of medium-voltage distribution network nodes. See step S4 in the above method for details.

[0064] The present invention also proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements steps S1 to S4 of the above-mentioned method for constructing and regulating the static voltage security domain of a medium-voltage distribution network.

[0065] The present invention also proposes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements steps S1 to S4 of the above-mentioned method for constructing and regulating the static voltage safety domain of a medium-voltage distribution network.

[0066] Example: like Figure 1 As shown, this example uses an improved IEEE 33-node distribution system for detailed analysis to verify the computational accuracy and performance of the proposed method. Large-scale distributed photovoltaic (PV) power sources are integrated into the medium-voltage distribution network to simulate the system's nonlinear characteristics and uncertainties. The specific connection locations and capacity configurations of the PV power sources in each medium-voltage distribution network are detailed in Table 1. Table 1 shows the PV connection locations and capacity configurations in different medium-voltage distribution networks (MVDNs) in this embodiment of the invention.

[0067] Table 1

[0068] The confidence interval for node voltage constraints is set to 0.94. The photovoltaic power injection follows a Beta distribution with shape parameters α and β, while the power injection from all loads follows a normal distribution with a standard deviation of 10% of the estimated mean. The upper and lower limits for system voltage are set to 1.05 pu and 0.95 pu, respectively, and the upper limit for current is set to 1.04 pu. Based on the probability distribution characteristics of node power injection, 1000 sample scenarios are randomly generated using the Monte Carlo method.

[0069] Next, the static voltage stability domain (SVSR) generation results based on data-driven power flow calculation (PF) are verified.

[0070] When the topology of a medium-voltage distribution network (MVDN) remains unchanged, matrix M can be regarded as a quasi-constant coefficient matrix.

[0071] Three power flow calculation methods were selected to compare the voltage regulation performance of the IEEE-33 node system: 1) Decoupled Linear Power Flow Method (DLPF): A simplified approximate solution to the classical nonlinear power flow equations; 2) Sensitivity-based linear power flow method (SLPF): It adopts linearized power flow equations derived by Taylor expansion, relies on accurate physical parameters and models, and calculates the plane slope at each operating point; 3) The method proposed in this invention.

[0072] Figure 2 The results of voltage regulation optimization using three power flow methods in the IEEE-33 node system are presented. As shown in the figure, DLPF, SLPF, and the method proposed in this invention can all provide feasible solutions, restoring the over-limit node voltage to a safe operating range.

[0073] Figure 3 The verification results of the optimized solutions for three power flow methods are shown (using exact nonlinear power flow verification) to evaluate the regulation accuracy of each method. Figure 3 The precise nonlinear power flow verification results show that the optimized solution of DLPF deviates significantly from the theoretical value, with the maximum node voltage reaching 1.044 per unit. This indicates that although DLPF can solve the voltage over-limit problem, its large voltage regulation range leads to artificially inflated optimization results for medium-voltage distribution networks, thereby increasing operating costs. Due to insufficient power flow calculation accuracy, SLPF cannot accurately achieve the expected voltage regulation target. In contrast, this method exhibits higher calculation accuracy, not only meeting the actual voltage regulation requirements but also possessing better applicability and stability.

[0074] In the improved IEEE 33-node system, node 15, with the largest photovoltaic capacity, was selected for analysis. The hyperplane coefficients of the SVSR boundary surface corresponding to the upper voltage limit of node 15 and the corresponding critical points are shown in Table 2. Table 2 shows the hyperplane coefficients and selected critical point values ​​required for generating the static safe region boundary of node 15 in this embodiment of the invention. Each boundary hyperplane expression in the table contains 32 pairs of hyperplane coefficients.

[0075] Table 2

[0076] To represent the Static Voltage Security Region (SVSR) in a two-dimensional plane, the power values ​​of unselected nodes are fixed at their critical values. Figure 4 A two-dimensional SVSR view of node 15 is shown. The feasible region formed by the overlap of the two regions is the static voltage safety region on the (P11, P14) plane. In the figure, the horizontal axis P11 represents the power fluctuation range of node 11, and the vertical axis P14 corresponds to the power variation range of node 14. The power fluctuations of these two nodes will affect the voltage level of node 15 and determine whether it remains within the safe range. The operating points inside and outside the region correspond to safe and unsafe voltage states, respectively, and no hole phenomena are found in the region, effectively verifying the correctness of characteristic 2.

[0077] To verify the accuracy of the constructed Static Voltage Security Domain (SVSR) boundary, this example uses the SVSR boundary generated by an AC power flow (AC PF) model based on precise parameters as the verification benchmark. The calculation method for the maximum boundary error in the node power injection space is shown in the following equation: (32), In the formula: This represents the total number of critical points used for comparison. Indicates the maximum boundary error. Let i be the i-th critical point on the boundary of the static voltage safety domain calculated by the precise parametric AC power flow model. This is the i-th critical point on the boundary of the static voltage safety domain generated by this method.

[0078] According to equation (32), the maximum error of the two-dimensional cross-section (P11, P14) is 0.741%. The error results for the other two-dimensional cross-sections are as follows: Figure 5 As shown, this method can obviously meet the accuracy requirements of practical engineering applications.

[0079] Table 3 compares the optimization results of the embodiments of the present invention, showing the optimization results of the objective function of the IEEE-33 node system obtained by the proposed method. A comparison with the optimization model based on precise parameters shows that the optimization results obtained by the two methods are highly consistent. Figure 6 As shown, the current in each branch is kept within the safe limit.

[0080] Table 3

[0081] Figure 7This paper demonstrates a stochastic chance-constrained voltage regulation process based on the SVSR (Stop-Voltage Regulator). The area outside the SVSR region represents voltage exceedance situations. Negative values ​​on the coordinate axis indicate that the node is absorbing reactive power. During voltage regulation, when the operating point is at point B, it is outside the SVSR region, indicating that the node voltage does not meet safety requirements, and voltage regulation cannot be completed using only node 24. Conversely, when the operating point is at point C, it is within the SVSR region, indicating that the node voltage is within the safe range, thus resolving the voltage exceedance problem. Compared to traditional point-by-point calculation methods, the proposed method can predict the regulation effect of the control equipment without performing additional power flow calculations.

[0082] To evaluate the voltage over-limit regulation performance of SVSR combined with the opportunity constraint method in medium-voltage distribution networks, 1000 over-limit scenarios were used to statistically verify weak voltage nodes. For example... Figure 8 As shown, the probability (defined as the pass probability) of each node voltage remaining within the preset constraint range can be obtained. Statistical results show that the pass rate of the voltage of the weak node exceeds the preset 0.94 confidence interval, and the pass rate of the voltage of the other nodes reaches 100%, verifying that the proposed method meets the accuracy requirements.

[0083] Although the functions and working processes of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific functions and working processes described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these are within the protection scope of the present invention.

Claims

1. A method for constructing and regulating the static voltage safety domain of a medium-voltage distribution network, characterized in that, Includes the following steps: S1, Constructing the static voltage security domain of the medium-voltage distribution network based on the physical model; S2, Based on historical operating data of the medium-voltage distribution network, obtain the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network mentioned above; S3. The stochastic chance constrained linear voltage optimization method is used to process the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network to obtain the stochastic chance constrained model of the static voltage security domain of the medium-voltage distribution network. S4. Based on the above stochastic chance constraint model, a voltage optimization model for medium-voltage distribution network nodes is constructed, and this model is used to optimize and control the real-time voltage of medium-voltage distribution network nodes.

2. The method for constructing and regulating the static voltage safety domain of a medium-voltage distribution network according to claim 1, characterized in that, The definition of the static voltage security domain of the medium-voltage distribution network in step S1 is as follows: （1）， In the formula, ; , representing any node in a medium-voltage distribution network The static voltage safety domain It is the set of all nodes in a medium-voltage distribution network; This represents the AC power flow equations at the root node under specified voltage magnitudes and phase angles. This represents the parameters of the equation; This represents a column vector composed of the voltages of each node in a medium-voltage distribution network. This represents a column vector composed of the minimum voltage values ​​at each node of a medium-voltage distribution network. This represents a column vector composed of the maximum voltage values ​​of each node in a medium-voltage distribution network.

3. The method for constructing and regulating the static voltage safety domain of a medium-voltage distribution network according to claim 1, characterized in that, The expression for the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network described in step S2 is as follows: （2）， In the formula, , representing the load power within a specific time period, vector and These represent column vectors composed of the active and reactive power of each branch in the medium-voltage distribution network, respectively. and The upper and lower limits of the hyperplane coefficients in the hyperplane boundary of the static voltage security domain of any node i in a medium-voltage distribution network are represented. and These represent the critical points at the upper and lower limits of active power, respectively. and These represent the critical points at the upper and lower limits of reactive power, respectively. This represents the function for dimension upscaling. and M1 and M2 represent the dimensionality-upgrading operation functions for the upper and lower critical points, respectively; M1 and M2 represent matrices, with M1 handling power differences and M2 handling nonlinear changes in the power grid state.

4. The method for constructing and regulating the static voltage safety domain of a medium-voltage distribution network according to claim 1, characterized in that, In step S3, a stochastic chance constrained linear voltage optimization method is used to process the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network to obtain a stochastic chance constrained model of the static voltage security domain of the medium-voltage distribution network. The specific process is as follows: At confidence level Under these conditions, ensure the voltage V at node j of the medium-voltage distribution network. j Not exceeding the upper limit or lower limit The general expression for opportunity constraints is: （3）， In the formula, Let be a probability function. and These represent the confidence levels for the upper and lower limits of the voltage constraints at node j, respectively. If we use column vectors and If the active and reactive power regulation of a node are represented respectively, then the model optimization process must follow the following constraints: （4）， （5） In the formula, G represents the set of nodes with controllable active power devices; H represents the set of nodes with controllable reactive power devices. and These represent the active power injection and reactive power injection at node j, respectively. and These represent the predicted active and reactive power injection values ​​for node j, respectively. This represents the active power adjustment amount at node j; This represents the reactive power adjustment amount at node j; Combining equations (3)-(5) with the hyperplane boundary model expression of the static voltage security domain of the medium-voltage distribution network, we obtain: （6）， In the formula, and Let represent the upper and lower bounds of the decision factors for node j, respectively. and These represent the reference active power and the reference reactive power, respectively. make , Formula (6) simplifies to the following formula (7): （7）， For a given Define the injection power probability distribution function for node j as follows. : （8）， Combining formulas (7) and (8), the opportunity constraints for safe voltage operation can be expressed as the following upper and lower limits: （9）， Given Having a monotonically increasing property, equation (9) can be equivalently transformed into equation (10): （10）， In the formula, for The inverse function; let The solution process is achieved through a combination of semi-invariant methods and Cornish-Fisher series expansion. The specific steps are as follows: Step S31: According to and Calculate the corresponding k-th order raw moments respectively. and ; Step S32: Based on the functional relationship between the different orders of semi-invariants and the origin moments shown in equation (11), calculate the k-th order semi-invariants of the predicted active and reactive power values ​​at node j. and ; （11）， Step S33: Calculate the node voltage magnitude k-th order semi-invariants; If random variables are independent, their semi-invariants have the following linear properties: node voltage amplitude The k-th order semi-invariant can be calculated from the semi-invariants of the node injected power. （12）， In the formula, This represents the power of node j at time k. This represents the coefficients associated with node j. and Indicates at time Time node Active power and reactive power, It is the set of all nodes in a medium-voltage distribution network. Indicates the total number of nodes; Step S34: Calculate the node voltage magnitude based on semi-invariants and Cornish-Fisher expansion method ; （13）， In the formula, , It is the standard normal distribution function; Formula (10) is solved through the linear optimization process of formulas (11)-(13) above to determine the upper and lower limits of the voltage at node j. and The corresponding chance constraint linear expressions for the upper and lower limits of the voltage at node j are obtained as follows (14), which is the stochastic chance constraint model of the static voltage security domain of the medium voltage distribution network. （14）， In the formula, and Representing nodes respectively j The upper and lower limits of the decision factors; and A column vector representing the active and reactive power regulation of each node; and Representing nodes respectively j Upper and lower limits of voltage.

5. The method for constructing and regulating the static voltage safety domain of a medium-voltage distribution network according to claim 1, characterized in that, The medium-voltage distribution network node voltage optimization model in step S4 includes an objective function and constraints. The objective function expression of the medium-voltage distribution network node voltage optimization model is as follows: （15）， The constraint expressions for the medium-voltage distribution network node voltage optimization model are as follows: （16）， In the formula, and These are column vectors representing the active and reactive power regulation quantities of each node, respectively. This represents the active power adjustment amount at node j; This represents the reactive power adjustment amount at node j; and Representing nodes respectively j The upper and lower limits of active power injection; and Representing nodes respectively j The upper and lower limits of reactive power injection; and These represent the predicted active and reactive power injection values ​​for node j, respectively. Indicates the current tap position of the on-load tap changer; and These represent the lower and upper limits of the on-load tap changer position, respectively. A column vector representing the rated voltage of each node; This represents a column vector composed of the voltage magnitudes of each node; This indicates the operating cost coefficient of the on-load tap changer; and These are auxiliary variables representing the positive and negative changes in the on-load tap changer position, respectively. M 1,j and M 2,j These represent two matrices, one for handling power differences and the other for handling nonlinear changes in grid conditions. and These represent the reference active power and the reference reactive power, respectively. ; This represents the function for dimension upscaling. Indicates the reference current; β 1 represents the coefficient between the change in current or power and the power adjustment; Indicates the upper limit of the line current; and These represent the active power and reactive power transmitted from node i to node j, respectively. and These represent the active power and reactive power transmitted from node j to node k, respectively. and Let G and H represent the active power injection and reactive power injection at node j, respectively; G represents the set of nodes with controllable active power devices; H represents the set of nodes with controllable reactive power devices. It is the set of all nodes in a medium-voltage distribution network; Let represent the set of downstream adjacent nodes of node j in a medium-voltage distribution network.

6. A device for constructing and regulating the static voltage safety domain of a medium-voltage distribution network based on the method for constructing and regulating the static voltage safety domain of a medium-voltage distribution network according to any one of claims 1 to 5, characterized in that, include: Static voltage security domain physical construction module: Constructs the static voltage security domain of medium-voltage distribution network based on physical model; Static voltage security domain data construction module: Based on historical operating data of medium-voltage distribution network, obtain the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network mentioned above; Stochastic chance constraint model construction module: The stochastic chance constraint linear voltage optimization method is used to process the hyperplane boundary model of the static voltage security domain of the medium-voltage distribution network to obtain the stochastic chance constraint model of the static voltage security domain of the medium-voltage distribution network. Node voltage optimization module: Based on the above stochastic chance constraint model, a node voltage optimization model for medium-voltage distribution network is constructed, and this model is used to optimize and control the real-time voltage of the nodes in the medium-voltage distribution network.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method for constructing and regulating the static voltage security domain of the medium-voltage distribution network as described in any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for constructing and regulating the static voltage safety domain of the medium-voltage distribution network as described in any one of claims 1 to 5.

Images